Question

Sarah's cake is very popular, so she decides to make another. This time however, she uses a circular cake pan to make a strawberry cake. When the cake is done, she doesn't cut it into pieces but she does put cream cheese frosting on top. If the cake pan is 6 inches deep and Sarah uses 154 in 2 of frosting, what is the surface area of the part of the cake that is not frosted? Use 22​/7 for π.

Answer 1

The surface area of the part of the cake that is not frosted is approximately -145.43 square inches.

Step-by-step explanation:

To find the surface area of the part of the cake that is not frosted, we need to subtract the area of the frosted part from the total surface area of the cake. Since the cake is circular, the surface area of the whole cake is given by the formula A = πr^2, where r is the radius of the cake pan. We know the depth of the pan is 6 inches, which means the height of the cake is 6 inches. So, the radius of the cake pan is half of the diameter, which is 6 inches. Therefore, the radius of the cake pan is 3 inches.

The total surface area of the cake is A = π(3^2) = 9π square inches. The area of the frosted part is given as 154 square inches.

To find the surface area of the part of the cake that is not frosted, we subtract the area of the frosted part from the total area of the cake: 9π - 154 = 9π - 154 square inches.

Calculating the approximate value: 9π - 154 = 9(3.14) - 154 ≈ 8.57 - 154 ≈ -145.43.